cosine transform

The Fourier cosine transform of a real function is the real part of the full complex Fourier transform, ℱ_x^(c)[f(x)](k) | = | ℜ[ℱ_x[f(x)](k)] | = | integral_(-∞)^∞ cos(2π k x) f(x) d x. The Fourier cosine transform F_c(k) of a function f(x) is implemented as FourierCosTransform[f, x, k], and different choices of a and b can be used by passing the optional FourierParameters -> {a, b} option. In this work, a = 0 and b = - 2π. The discrete Fourier cosine transform of a list l of real numbers can be computed in the Wolfram Language using FourierDCT[l].

Fourier sine transform | Fourier transform